The Blues signed Michel from Sporting Gijon and Craig Gardner from Aston Villa in the January transfer window.
McLeish will be backed by the finances of new owner Carson Yeung.
Dunford said: “I expect it to be quite a busy summer. We will gear ourselves up for what I’m sure will be significant transfer movement in the summer.
“There are also eight or nine players likely to be leaving the club which means from a numerical point of view, we need new players of quality to supplement the ones we have got as well.”
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Summer 2016 is set to be a very exciting time for football fans, as this is when the long awaited Euro 2016 tournament kicks off.
Since Guus Hiddink arrived at the helm, Chelsea have improved considerably after a tricky start to the campaign.